For the squared distortion communications system of Example 8.14 with v = 1.5 and d = 0.5, find the value of T that minimizes PERR.
Example 8.14
A digital communications system transmits either a bit B = 0 or B = 1 with probability 1/2. The internal circuitry of the receiver results in a "squared distortion" such that received signal (measured in volts) is either:
Where N, the noise is Gaussian (0, 1). For each bit transmitted, the receiver produces an output 
= 0 if X ≤ T and an output = 1, otherwise. Simulate the transmission of 20, 000 bits through this system with v = 1.5 volts, d = 0.5 and the following values of the decision threshold: T = -0.5, -0.2, 0, 0.2, 0.5 volts. Which choice of T produces the lowest probability of error? Can you find a value of T that does a better job?